Wave-mean Flow Interaction Research Articles

Can zonally symmetric inertial waves drive an oscillating zonal mean flow?

In the present paper zonal mean flow excitation by inertial waves is studied in analogy to mean flow excitation by gravity waves that plays an important role for the quasi-biennial oscillation in the equatorial atmosphere. In geophysical flows that are stratified and rotating, pure gravity and inertial waves correspond to the two limiting cases: gravity waves neglect rotation, inertial waves neglect stratification. The former are more relevant for fluids like the atmosphere, where stratification is dominant, the latter for the deep oceans or planet cores, where rotation dominates. In the present study a hierarchy of simple analytical and numerical models of zonally symmetric inertial wave-mean flow interactions is considered and the results are compared with data from a laboratory experiment. The main findings can be summarised as follows: (i) when the waves are decoupled from the mean flow they just drive a retrograde (eastward) zonal mean flow, independent of the sign of the meridional phase speed; (ii) when coupling is present and the zonal mean flow is assumed to be steady, the waves can drive vertically alternating jets, but still, in contrast to the gravity wave case, the structure is independent of the sign of the meridional phase speed; (iii) when coupling is present and time-dependent zonal mean flows are considered the waves can drive vertically and temporarily oscillating mean flows. The comparison with laboratory data from a rotating annulus experiment shows a qualitative agreement. It appears that the experiment captures the basic elements of the inertial wave mean flow coupling. The results might be relevant to understand how the Equatorial Deep Jets can be maintained against dissipation, a process currently discussed controversially.

Interannual and intraseasonal variability of stratospheric dynamics and stratosphere–troposphere coupling during northern winter

The UK Met Office reanalysis data have been used to investigate the interannual and intraseasonal variability of the stratospheric dynamics and thermal structure. The results obtained show that the maximum of interannual variability of the mean zonal flow associated with the quasi-biennial oscillation (QBO) is observed at the altitude of about 30km. It is shown that there is a statistically significant influence of the QBO phase on the extratropical stratosphere, the so-called, Holton–Tan effect. The results of data analysis show that the conditions under the easterly QBO phase are more favorable for the development of the sudden stratospheric warmings (SSW). The statistical analysis of 15 major SSW observed during two last decades has been performed. The obtained results demonstrate that in recent years internal processes associated with nonlinear interactions of stationary planetary waves (SPW) with the mean flow played a dominant role. It is shown that the first enhancement of the SPW1 in the upper stratosphere takes place because of an amplification of nonlinear interactions between this wave and the mean flow. This enhancement is accompanied by a subsequent increase in the wave activity flux from the stratosphere into the troposphere with further redistribution of wave activity in the horizontal plane. Then, an increase of the upward flux from the troposphere into the stratosphere in another region occurs. The secondary enhancement of the planetary wave activity in the stratosphere is accompanied by the heating of the polar region and the weakening, or even reversal of the stratospheric jet. Additionally to the well-known result that meridional refraction of SPW to the polar region in stratosphere is one of the preconditions of development SSW, the nonlinear wave–wave and wave–mean flow interactions can play an important role before and during SSW. It is shown that the upper stratosphere can be considered as the region where SPW2 is generated during SSW.

Instability mechanisms in a low-Mach-number reacting flow from coupled convection-reaction-diffusion equations

In this paper, instability mechanisms in a low Mach number reacting flow are investigated. Here, the emphasis is on the growth or decay of acoustic oscillations which arise from the acoustic-hydrodynamic interaction in a low Mach number reacting flow. Motivated by the studies in magnetohydrodynamics and atmospheric flows, we propose to investigate the acoustic-hydrodynamic coupling as a system of wave-mean flow interaction. For example, a comparison with the heat fluctuation modified hydrodynamics associated with magnetohydrodynamics is useful in understanding this coupling. The wavelike acoustic disturbance is introduced here as a compressibility correction to the mean flow. Accounting for the multiple scales introduced by the weak compressibility, we derive a set of equations governing wave-mean flow interaction in a reacting low Mach number flow. Sources such as volume expansion (which, in atmospheric flows arises due to the density variation with altitude) occur in reacting flows due to the heat release rate. This heat release rate, when coupled with the acoustic field, often leads to self-sustained thermo-acoustic oscillations. In the study of such oscillations, we discover a relation between the acoustic pressure and second order thermal fluctuations. Further, using this relation, we discover the nonlinear coupling mechanism that would lead to self-sustained oscillations in a reacting low Mach number flow. This mechanism, represented by a coupled convection reaction diffusion system, is presented here for the first time. In addition to the acoustic pressure and temperature fields, we also discover the role of acoustic velocity field in the acoustic-hydrodynamic interaction through a convective and lift-up mechanism.

A simulated lagged response of the North Atlantic Oscillation to the solar cycle over the period 1960–2009

Numerous studies have suggested an impact of the 11 year solar cycle on the winter North Atlantic Oscillation (NAO), with an increased tendency for positive (negative) NAO signals to occur at maxima (minima) of the solar cycle. Climate models have successfully reproduced this solar cycle modulation of the NAO, although the magnitude of the effect is often considerably weaker than implied by observations. A leading candidate for the mechanism of solar influence is via the impact of ultraviolet radiation variability on heating rates in the tropical upper stratosphere, and consequently on the meridional temperature gradient and zonal winds. Model simulations show a zonal mean wind anomaly that migrates polewards and downwards through wave–mean flow interaction. On reaching the troposphere this produces a response similar to the winter NAO. Recent analyses of observations have shown that solar cycle–NAO link becomes clearer approximately three years after solar maximum and minimum. Previous modelling studies have been unable to reproduce a lagged response of the observed magnitude. In this study, the impact of solar cycle on the NAO is investigated using an atmosphere–ocean coupled climate model. Simulations that include climate forcings are performed over the period 1960–2009 for two solar forcing scenarios: constant solar irradiance, and time-varying solar irradiance. We show that the model produces significant NAO responses peaking several years after extrema of the solar cycle, persisting even when the solar forcing becomes neutral. This confirms suggestions of a further component to the solar influence on the NAO beyond direct atmospheric heating and its dynamical response. Analysis of simulated upper ocean temperature anomalies confirms that the North Atlantic Ocean provides the memory of the solar forcing required to produce the lagged NAO response. These results have implications for improving skill in decadal predictions of the European and North American winter climate.

Coupling in the middle atmosphere related to the 2013 major sudden stratospheric warming

Abstract. The previously reported observation of anomalous eastward gravity wave forcing at mesopause heights around the onset of the January 2013 major sudden stratospheric warming (SSW) over Trondheim, Norway (63° N, 10° E), is placed in a global perspective using Microwave Limb Sounder (MLS) temperature observations from the Aura satellite. It is shown that this anomalous forcing results in a clear cooling over Trondheim about 10 km below mesopause heights. Conversely, near the mesopause itself, where the gravity wave forcing was measured, observations with meteor radar, OH airglow and MLS show no distinct cooling. Polar cap zonal mean temperatures show a similar vertical profile. Longitudinal variability in the high northern-latitude mesosphere and lower thermosphere (MLT) is characterized by a quasi-stationary wave-1 structure, which reverses phase at altitudes below ~ 0.1 hPa. This wave-1 develops prior to the SSW onset, and starts to propagate westward at the SSW onset. The latitudinal pole-to-pole temperature structure associated with the major SSW shows a warming (cooling) in the winter stratosphere (mesosphere) which extends to about 40° N. In the stratosphere, a cooling extending over the equator and far into the summer hemisphere is observed, whereas in the mesosphere an equatorial warming is noted. In the Southern Hemisphere mesosphere, a warm anomaly overlaying a cold anomaly is present, which is shown to propagate downward in time. This observed structure is in accordance with the temperature perturbations predicted by the proposed interhemispheric coupling mechanism for cases of increased winter stratospheric planetary wave activity, of which major SSWs are an extreme case. These results provide observational evidence for the interhemispheric coupling mechanism, and for the wave-mean flow interaction believed to be responsible for the establishment of the anomalies in the summer hemisphere.

The slowly evolving background state of the atmosphere

The theory of wave–mean flow interaction requires a partition of the atmospheric flow into a notional background state and perturbations to it. Here, a background state, known as the Modified Lagrangian Mean (MLM), is defined as the zonally symmetric state obtained by requiring that every potential vorticity (PV) contour lying within an isentropic layer encloses the same mass and circulation as in the full flow. For adiabatic and frictionless flow, these two integral properties are time‐invariant and the MLM state is a steady solution of the primitive equations. The time dependence in the adiabatic flow is put into the perturbations, which can be described by a wave‐activity conservation law that is exact even at large amplitude. Furthermore, the effects of non‐conservative processes on wave activity can be calculated from the conservation law.A new method to calculate the MLM state is introduced, where the position of the lower boundary is obtained as part of the solution. The results are illustrated using Northern Hemisphere ERA‐Interim data. The MLM state evolves slowly, implying that the net non‐conservative effects are weak. Although ‘adiabatic eddy fluxes’ cannot affect the MLM state, the effects of Rossby‐wave breaking, PV filamentation and subsequent dissipation result in sharpening of the polar vortex edge and meridional shifts in the MLM zonal flow, both at tropopause level and on the winter stratospheric vortex. The rate of downward migration of wave activity during stratospheric sudden warmings is shown to be given by the vertical scale associated with polar vortex tilt divided by the time‐scale for wave dissipation estimated from the wave‐activity conservation law. Aspects of troposphere–stratosphere interaction are discussed.The new framework is suitable to examine the climate and its interactions with disturbances, such as midlatitude storm tracks, and makes a clean partition between adiabatic and non‐conservative processes.

Dynamic Balances in a Wavy Boundary Layer

Abstract The authors analyze the influence of waves on the budgets of momentum flux and kinetic energy in the atmospheric flow over sea surface waves and use the findings to reinterpret the results from the earlier empirical studies on the subject. This analysis employs the framework of wave–mean flow interaction and experimental data collected recently over the open ocean. From a minimal set of plausible assumptions, limited to small-slope waves and uncorrelated turbulent and wave-induced motions in the wind, this study demonstrates that the budgets apply separately to the turbulent and the wave-induced flows. The explicit forms of the wave-supported fluxes of momentum and kinetic energy favor wave spectra ∝ ω−β, 4 ≤ β ≤ 5 for wind–wave equilibrium. These explicit forms also show that in common conditions at heights above one significant wave height from the unperturbed surface, the wave-supported fluxes are a small fraction of the total, of the order of 5%. The wave influence on the kinetic energy budget and on the shape of the wind profile is therefore also small at these heights and thus difficult to identify experimentally next to influences from nonstationarity or horizontal inhomogeneity. Consequently, the predictions of Monin–Obukhov phenomenology show little sensitivity to wave effects. This makes the phenomenology as valid over the ocean as it is over land, but a poor instrument for studying wind–wave interaction. Describing the wind–wave interaction through the dynamics and statistics of the wave-induced motion remains a viable and productive alternative.

Stratospheric Wave–Mean Flow Feedbacks and Sudden Stratospheric Warmings in a Simple Model Forced by Upward Wave Activity Flux

Abstract A classic result of studying stratospheric wave–mean flow interactions presented by Holton and Mass is that, for constant incoming wave forcing (at a notional tropopause), a vacillating stratospheric response may ensue. Simple models, such as the Holton–Mass model, typically prescribe the incoming wave forcing in terms of geopotential perturbation, which is not a proxy for upward wave activity flux. Here, the authors reformulate the Holton–Mass model such that incoming upward wave activity flux is prescribed. The Holton–Mass model contains a positive wave–mean flow feedback whereby wave forcing decelerates the mean flow, allowing enhanced wave propagation, which then further decelerates the mean flow, etc., until the mean flow no longer supports wave propagation. By specifying incoming wave activity flux, this feedback is constrained to the model interior. Bistability—where the zonal wind may exist at one of two distinct steady states for a given incoming wave forcing—is maintained in this reformulated model. The model is perturbed with transient pulses of upward wave activity flux to produce transitions between the two stable states. A minimum of integrated incoming wave activity flux necessary to force these sudden stratospheric warming–like transitions exists for pulses with time scales on the order of 10 days, arising from a wave time scale internal to the model at which forcing produces the strongest mean-flow response. The authors examine how the tropopause affects the internal feedback for this model setup and find that the tropopause inversion layer may potentially provide an important source of wave activity in the lower stratosphere.

Summer Arctic Atmospheric Circulation Response to Spring Eurasian Snow Cover and Its Possible Linkage to Accelerated Sea Ice Decrease

Abstract Anticyclonic circulation has intensified over the Arctic Ocean in summer during recent decades. However, the underlying mechanism is, as yet, not well understood. Here, it is shown that earlier spring Eurasian snowmelt leads to anomalously negative sea level pressure (SLP) over Eurasia and positive SLP over the Arctic, which has strong projection on the negative phase of the northern annular mode (NAM) in summer through the wave–mean flow interaction. Specifically, earlier spring snowmelt over Eurasia leads to a warmer land surface, because of reduced surface albedo. The warmed surface amplifies stationary Rossby waves, leading to a deceleration of the subpolar jet. As a consequence, rising motion is enhanced over the land, and compensating subsidence and adiabatic heating occur in the Arctic troposphere, forming the negative NAM. The intensified anticyclonic circulation has played a contributing role in accelerating the sea ice decline observed during the last two decades. The results here provide important information for improving seasonal prediction of summer sea ice cover.

The Continuous Mutual Evolution of Equatorial Waves and the Quasi-Biennial Oscillation of Zonal Flow in the Equatorial Stratosphere*

Abstract The continuous mutual evolution of equatorial waves and the background quasi-biennial oscillation (QBO) is demonstrated using daily NCEP–U.S. Department of Energy (DOE) reanalysis for the period from 1 January 1979 to 31 December 2010. Using a novel diagnostic technique, the phase speed, vertical tilting, and form stress of equatorial waves in the stratosphere are obtained continuously on a daily basis. The results indicate that, on top of a weak-amplitude annual-cycle signal, all of these wave properties have a pronounced QBO signal with a downward propagation that evolves continuously together with the background QBO. The analysis also highlights the potential role of wave-induced form stress in driving the QBO regime change. Dominant waves in the equatorial stratosphere propagate very slowly relative to the ground at all times, implying that their observed intrinsic phase speed evolution follows the background QBO nearly exactly but with opposite sign, as the established theory predicts. By revealing the continuous evolution of the form stress associated with the vertically tilted waves, the new diagnostic method also demonstrates the dominance of eastward-tilted, eastward-propagating waves contributing to a deceleration of easterly flow at high altitudes, which causes a downward propagation of the easterly flow signal. Similarly, the dominance of westward-tilted, westward-propagating waves acts to reverse westerly flow to easterly flow and causes a downward propagation of westerly flow signal. The results suggest that in addition to the wave-breaking processes, such continuously alternating downward transfer of westerly and easterly angular momentum by westward-tilted, westward-propagating waves and eastward-tilted, eastward-propagating waves contributes to the wave–mean flow interaction mechanism for the QBO.

Angular momentum transport by stochastically excited oscillations in rapidly rotating massive stars

We estimate the amount of angular momentum transferred by the low-frequency oscillations detected in the rapidly rotating hot Be star HD 51452. Here, we assume that the oscillations detected are stochastically excited by convective motions in the convective core of the star, that is, we treat the oscillations as forced oscillations excited by the periodic convective motions of the core fluids having the frequencies observationally determined. With the observational amplitudes of the photometric variations, we determine the oscillation amplitudes, which makes it possible to estimate the net amount of angular momentum transferred by the oscillations using the wave-meanflow interaction theory. Since we do not have any information concerning the azimuthal wavenumber $m$ and spherical harmonic degree $l$ for each of the oscillations, we assume that all the frequencies detected are prograde or retrograde in the observer's frame and they are all associated with a single value of $m$ both for even modes ($l=|m|$) and for odd modes ($l=|m|+1$). We estimate the amount of angular momentum transferred by the oscillations for $|m|=1$ and 2, which are typical $|m|$ values for Be stars, and find that the amount is large enough for a decretion disc to form around the star. Therefore, transport of angular momentum by waves stochastically excited in the core of Be stars might be responsible for the Be phenomenon.

On the Role of Asymmetric Convective Bursts to the Problem of Hurricane Intensification: Radiation of Vortex Rossby Waves and Wave–Mean Flow Interactions

Abstract The role of asymmetric convection to the intensity change of a weak vortex is investigated with the aid of a “dry” thermally forced model. Numerical experiments are conducted, starting with a weak vortex forced by a localized thermal anomaly. The concept of wave activity, the Eliassen–Palm flux, and eddy kinetic energy are then applied to identify the nature of the dominant generated waves and to diagnose their kinematics, structure, and impact on the primary vortex. The physical reasons for which disagreements with previous studies exist are also investigated utilizing the governing equation for potential vorticity (PV) perturbations and a number of sensitivity experiments. From the control experiment, it is found that the response of the vortex is dominated by the radiation of a damped sheared vortex Rossby wave (VRW) that acts to accelerate the symmetric flow through the transport of angular momentum. An increase of the kinetic energy of the symmetric flow by the VRW is shown also from the eddy kinetic energy budget. Additional tests performed on the structure and the magnitude of the initial thermal forcing confirm the robustness of the results and emphasize the significance of the wave–mean flow interaction to the intensification process. From the sensitivity experiments, it is found that for a localized thermal anomaly, regardless of the baroclinicity of the vortex and the radial and vertical gradients of the thermal forcing, the resultant PV perturbation follows a damping behavior, thus suggesting that deceleration of the vortex should not be expected.

Isentropic Analysis of Polar Cold Airmass Streams in the Northern Hemispheric Winter

Abstract An analysis method is proposed for polar cold airmass streams from generation to disappearance. It designates a threshold potential temperature θT at around the turning point of the extratropical direct (ETD) meridional circulation from downward to equatorward in the mass-weighted isentropic zonal mean (MIM) and clarifies the geographical distributions of the cold air mass, the negative heat content (NHC), their horizontal fluxes, and their diabatic change rates on the basis of conservation relations of the air mass and thermodynamic energy. In the Northern Hemispheric winter, the polar cold air mass below θT = 280 K has two main streams: the East Asian stream and the North American stream. The former grows over the northern part of the Eurasian continent, flows eastward, turns down southeastward toward East Asia via Siberia, and disappears over the western North Pacific Ocean. The latter grows over the Arctic Ocean, flows toward the eastern coast of North America via Hudson Bay, and disappears over the western North Atlantic Ocean. In their exit regions, wave–mean flow interactions are considered to transfer the angular momentum from the cold airstreams to the upward Eliassen–Palm flux and convert the available potential energy to wave energy.

Planetary Waves - Major Forcing Agent in Generating Stratospheric and Mesospheric Quasi Biennial Oscillation

Quasi Biennial Oscillation (QBO) and Semi Annual Oscillation (SAO) are dominant natural oscillations in the equatorial lower stratosphere and mesosphere and are believed to be generated by the wave-mean flow interaction. The characteristics of stratospheric QBO (SQBO) and mesospheric QBO (MQBO) and SAO are studied by making use of the monthly mean zonal and meridional winds derived from four decades of balloon (1970-2010) and rocket (1971-2007) flights and seven years of SKiYMET meteor radar (2004-2011) observations over an equatorial station Thiruvananthapuram. The year-to-year variation and interrelationships between these oscillations are also studied. The quantitative estimation of forcing towards the mean flow acceleration producing the maximum phase of SQBO during the four-decade period shows 70-80% contribution from planetary waves, while during minimum phase of SQBO the contribution is 30-35%. It is also found that the contribution by planetary waves towards the mean flow acceleration producing MQBO maximum during the seven-year period is around 30-90% and during MQBO minimum phase it is 30-60%. The vertical structure of these oscillations present over the equatorial station is also derived.

On Langmuir circulation in shallow waters

AbstractThe instability of shallow-water waves on a moderate shear to Langmuir circulation is considered. In such instances, specifically at the shallow end of the inner coastal region, the shear can significantly affect the drift giving rise to profiles markedly different from the simple Stokes drift. Since drift and shear are instrumental in the instability to Langmuir circulation, of key interest is how that variation in turn affects onset to Langmuir circulation. Also of interest is the effect on onset of various boundary conditions. To that end the initial value problem describing the wave–mean flow interaction which accounts for the multiple time scales of the surface waves, evolving shear and evolving Langmuir circulation is crafted from scratch, and includes the wave-induced drift and a consistent set of free-surface boundary conditions. The problem necessitates that Navier–Stokes be employed side by side with a set of mean-field equations. Specifically, the former is used to evaluate events with the shortest time scale, that is the wave field, while the mean field set is averaged over that time scale. This averaged set, the CLg equations, follow from the generalized Lagrangian mean equations and for the case at hand take the same form as the well-known CL equations, albeit with different time and velocity scales. Results based upon the Stokes drift are used as a reference to which those based upon drift profiles corrected for shear are compared, noting that the latter are asymptotic to the former as the waves transition from shallow to deep. Two typical temporal flow fields are considered: shear-driven flow and pressure-driven flow. Relative to the reference case, shear-driven flow is found to be destabilizing while pressure driven are stabilizing to Langmuir circulation. In pressure-driven flows it is further found that multiple layers, as opposed to a single layer, of Langmuir circulation can form, with the most intense circulations at the ocean floor. Moreover, the layers can extend into a region of flow beyond that in which the instability applies, suggesting that Langmuir circulation excited by the instability can in turn drive, as a dynamic consequence, contiguous albeit less intense Langmuir circulation. Pressure-driven flows also admit two preferred spacings, one closely in accord with observation for small-aspect-ratio Langmuir circulation, the other well in excess of observed large-aspect-ratio Langmuir circulation.

The Impact of Baroclinic Eddy Feedback on the Persistence of Jet Variability in the Two-Layer Model

Abstract Although it is well known that the persistence of extratropical jet shifts is enhanced by a positive eddy feedback, the dynamics of this feedback is still debated. Two types of mechanisms have been proposed: barotropic mechanisms rely on changes in upper-level propagation and baroclinic mechanisms rely on the coupling between barotropic and baroclinic flow. Recent studies have suggested that barotropic models can capture key aspects of the observed jet variability but the role of baroclinic dynamics has been less explored. This study investigates the temporal relations between barotropic and baroclinic anomalies and their eddy forcings during the internal variability of the simple two-layer quasigeostrophic model. A large correlation is found between barotropic and baroclinic anomalies and between the meridional and vertical components of the Eliassen–Palm divergence, especially at low frequency. The low-frequency variability is consistent with the baroclinic mechanism: persistent upper-level eddy momentum convergence is associated with (and precedes) persistent anomalies in the poleward eddy heat flux. In contrast, at high frequency, poleward heat flux anomalies are associated with eddy momentum divergence aloft and both eddy forcings have same-sign contributions to the upper-level eddy potential vorticity (PV) flux. In this limit the eddy PV flux is associated with wave activity transience as effective diffusivity is too small to dissipate the wave–mean flow interaction term. The large correlation between barotropic and baroclinic anomalies implies that the low-frequency variability of barotropic flow may be affected by thermal damping when this damping is sufficiently strong. For example, zonal index persistence drops drastically in our model when baroclinicity shifts are prevented by strong thermal restoration.

Sensitivity of stratospheric dynamics and chemistry to QBO nudging width in the chemistry‒climate model WACCM

The consequences of different quasi‒biennial oscillation (QBO) nudging widths on stratospheric dynamics and chemistry are analyzed by comparing two model simulations with the National Center for Atmospheric Research's Whole Atmosphere Community Climate Model (WACCM) where the width of the QBO is varied between 22° and 8.5° north and south. The sensitivity to the nudging width is strongest in Northern Hemisphere (NH) winter where the Holton‒Tan effect in the polar stratosphere, i.e., stronger zonal mean winds during QBO west phases, is enhanced for the wider compared to the narrower nudging case. The differences between QBO west and east conditions for the two model experiments can be explained with differences in wave propagation, wave‒mean flow interaction, and the residual circulation. In the wider nudging case, a divergence anomaly in the midlatitude upper stratosphere/lower mesosphere occurs together with an equatorward anomaly of the residual circulation. This seems to result in a strengthening of the meridional temperature gradient and hence a significant strengthening of the polar night jet (PNJ). In the narrower nudging case, these circulation changes are weaker and not statistically significant, consistent with a weaker and less significant impact on the PNJ. Chemical tracers like ozone, water vapor, and methane react accordingly. From a comparison of westerly minus easterly phase composite differences in the model to reanalysis and satellite data, we conclude that the standard WACCM configuration (QBO22) generates more realistic QBO effects in stratospheric dynamics and chemistry during NH winter. Our study also confirms the importance of the secondary mean meridional circulation associated with the QBO for the Holton‒Tan effect.

Spontaneous QBO-like oscillations in an atmospheric model dynamical core

[1] The ability of general circulation models (GCMs) to simulate the quasi-biennial oscillation (QBO) is an important model characteristic. Typically, the moist convective parameterization is believed to be the key GCM component that triggers tropical waves, thereby forcing wave-mean flow interactions. We show that QBO-like oscillations can also be simulated in a dry dynamical core driven by the Held-Suarez forcing. No gravity wave drag parameterization is applied. The simulations utilize the semi-Lagrangian spectral transform dynamical core of National Center for Atmospheric Research's Community Atmosphere Model. The QBO-like signal has a long period between 42–45 months and occurs in the upper stratosphere; different from observations. However, the amplitudes, asymmetries, and meridional extent closely resemble the observed QBO. Wave-number frequency analysis shows that resolved equatorially trapped waves are abundant despite the absence of cumulus convection. A Transformed Eulerian-Mean analysis suggests that the divergence of the Eliassen-Palm flux and vertical advection provide most of the forcing counteracted by diffusion.

Avalanches, breathers, and flow reversal in a continuous Lorenz-96 model

For the discrete model suggested by Lorenz in 1996, a one-dimensional long-wave approximation with nonlinear excitation and diffusion is derived. The model is energy conserving but non-Hamiltonian. In a low-order truncation, weak external forcing of the zonal mean flow induces avalanchelike breather solutions which cause reversal of the mean flow by a wave-mean flow interaction. The mechanism is an outburst-recharge process similar to avalanches in a sandpile model.

On the Mechanism Underlying the Spontaneous Emergence of Barotropic Zonal Jets

Abstract Zonal jets are commonly observed to spontaneously emerge in a β-plane channel from a background of turbulence that is sustained in a statistical steady state by homogeneous stochastic excitation and dissipation of vorticity. The mechanism for jet formation is examined in this work within the statistical wave–mean flow interaction framework of stochastic structural stability theory (SSST) that makes predictions for the emergence of zonal jets in β-plane turbulence. Using the coupled dynamical SSST system that governs the joint evolution of the second-order statistics and the mean flow, the structural stability of the spatially homogeneous statistical equilibrium with no mean zonal jets is studied. It is shown that close to the structural stability boundary, the eddy–mean flow dynamics can be split into two competing processes. The first, which is shearing of the eddies by the local shear described by Orr dynamics in a β plane, is shown in the limit of infinitesimal shear to lead to the formation of jets. The second, which is momentum flux divergence resulting from lateral wave propagation on the nonuniform local mean vorticity gradient, is shown to oppose jet formation. The upgradient momentum fluxes due to shearing of the eddies are shown to act exactly as negative viscosity for an anisotropic forcing and as negative hyperviscosity for isotropic forcing. The downgradient fluxes due to wave flux divergence are shown to act hyperdiffusively.